Stewart Heitmann

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The Brain Dynamics Toolbox is open-source software for simulating dynamical
systems in neuroscience. It is for researchers and students who wish to
explore mathematical models of brain function using Matlab. It includes
a graphical tool for simulating dynamical systems in real-time as well
as command-line tools for scripting large-scale simulations.

Optogenetic techniques allow neurophysiologists to directly stimulate neurons with light. It is often assumed that the dynamical behaviour of the neural tissue is unchanged. However recent observations of optogenetically-induced travelling waves provide a clue that this may not be the case. Lu et al (2015) found that constant stimulation of macaque cortex elicited 40-80 Hz oscillations in the local field potential in a manner consistent with Type II neural excitability. Furthermore, those oscillations propagated far into the surrounding cortical tissue well beyond the reach of the stimulation.

Mathematical theory suggests that only neural tissue with Type I excitability can sustain propagating waves. So how can cortical tissue simultaneously exhibit both Type I and Type II excitability? We investigated the apparent contradiction by modelling the cortex as recurrently-connected excitatory and inhibitory neurons. Such models exhibit either Type I or Type II excitability depending upon the choice of parameters. We found that optogenetic stimulation can locally transform Type I excitability into Type II excitability by preferentially targeting inhibitory cells. The findings shed new light on how optogenetic stimulation can alter the response dynamics of neural tissue.

Space-time plots of the cortical model in one spatial dimension. Optogenetic stimulation was applied focally at position x=0. Panels A-C show cases of weak, medium, and strong stimulation respectively. 40-80 Hz oscillations arose gradually from the stimulation site via Type II excitability. Waves were emitted from the stimulation site via Type I excitability once the simulation reached a critical threshold. The simulated medium thus exhibited co-existing Type I and Type II excitability in agreement with neurophysiological observations.

Geometric patterns of spirals, honeycombs and checker-boards are common themes in visual hallucinations. They are thought to originate from the neural circuitry of the primary visual cortex -- the region of the brain which processes visual shapes.

Our collaborators at the University of New South Wales devised a clever method for objectively measuring the visual hallucinations seen in stroboscopic flicker. In particular, they measured the spatial wavelength and speed of illusory blobs that appear to race around a ring-shaped stimulus when it is flickered at 10-20 Hz. As part of this study, we constructed a mathematical model of the visual cortex that reproduces much of the perceptual behaviour of the hallucinations.

The prevalence of
synchronized neural spiking in the brain suggests a role in normal brain
function. Neural synchronization can be modelled with coupled
oscillators where the phase of each oscillator represents the timing of
the neural spike. These models generate planar waves and spirals which
resemble those observed in neural tissue. We recently characterized a
new synchronization solution that we call ripple. Ripple is
topologically distinct from waves and spirals and constitutes another
possibility in neural synchronization.

Beta-band (15-30
Hz) neural oscillations are routinely observed in the human motor system
but their purpose is unknown. We conjectured that the spatial arrangement of beta oscillations in cortex could serves as the neural substrate for encoding motor commands. We constructed a model of the descending motor system which shows how oscillatory patterns in cortex can be translated into specific muscle
movements. The model demonstrates a functional role for beta oscillations that also replicates the known physiological changes of beta-band cortico-muscular coherence during movement.

Co-contraction refers to the simultaneous contraction of antagonist muscles. It has no impact on joint torque but it does increase joint damping because of the non-linear force-velocity properties of muscle tissue.

We analysed the stability of co-contracting muscle in a simulated biomechanical limb with realistic force-length-velocity relationships. We found that co-contraction not only modulates joint damping but that it also effects postural stability. Under certain conditions, co-contracting muscles can even induce multiple stable equilibrium points.